Determine the limit:
lim x→−3 √ (x^2 + 7 − 4)/(x^2 − 9)
So I'm pretty sure it doesn't exist but i just wanted to make sure... i got it down to
√(x^2+3)/(x+3)(x-3)
which doesn't exist because it equals zero
thanks for any help
For convenience, let f(x) = √(x^2+3)/(x+3)(x-3).
Note that $\displaystyle \lim_{x \rightarrow -3^+} f(x) = -\infty$ but $\displaystyle \lim_{x \rightarrow -3^-} f(x) = + \infty$.
The left hand limit does not equal the right hand limit.
Therefore $\displaystyle \lim_{x \rightarrow -3} f(x) = +\infty$ does not exist.